This paper describes the development of a high speed dynamic simulator for humanoid robots. In the simulator, an order n formulation is used to solve the inverse dynamics and forward dynamics of a multi-body system. The formulation can deal with a tree structure and multiple contacts with the environment. In order to simulate a collision with friction between the bodies and environments, a virtual spring-damper contact model is proposed. This model enables an accurate computation of the reaction forces and slips. A simulation of ascending steep stairs is carried out in order to demonstrate the validity of the simulation. The results of the simulation are presented and discussed.
